The pressure inside two soap bubbles are 1.02 atm. and 1.03 atm. respectively. Atmospheric pressure is 1 atm. The ratio of their volumes is -

Question

The pressure inside two soap bubbles are 1.02 atm. and 1.03 atm. respectively. Atmospheric pressure is 1 atm. The ratio of their volumes is - (A) 102: 103 (B) 9: 4 (C) (103)3:(102)3 (D) 27: 8

Tardigrade Admin · Accepted Answer

P in - P atm = excess pressure =(4 T / R ) ∴ ( R 1/ R 2)=(Δ P 2/Δ P 1)=(3/2) ∴ ( V 1/ V 2)=( R 13/ R 23)=(27/8)

Q. The pressure inside two soap bubbles are $1.02$ atm. and $1.03 a t m$ . respectively. Atmospheric pressure is $1 a t m$ . The ratio of their volumes is -

$102 : 103$

$9 : 4$

$(103)^{3} : (102)^{3}$

$27 : 8$

$P_{in} - P_{a t m} =$ excess pressure $= \frac{4 T}{R}$
$∴ \frac{R _{1}}{R _{2}} = \frac{Δ P _{2}}{Δ P _{1}} = \frac{3}{2}$
$∴ \frac{V _{1}}{V _{2}} = \frac{R _{1}^{3}}{R _{2}^{3}} = \frac{27}{8}$

Q. The pressure inside two soap bubbles are 1.02 atm. and 1.03atm. respectively. Atmospheric pressure is 1atm. The ratio of their volumes is -

102:103

9:4

(103)3:(102)3

27:8